Question

When Sam and his friends get together, Sam makes orange soda by mixing orange juice with soda (sparkling water). On Friday, Sam makes 7 liters of orange soda by mixing 3 liters of orange juice with 4 liters of soda.On Saturday, Sam makes 9 liters of orange soda by mixing 4 liters of orange juice with5 liters of soda. Make a prediction about how the two orange sodas will compare in taste. Explain your reasoning.

Answer 1

Friday's drink will taste more like soda and Saturday's drink will taste more like orange juice.

Explanation:

Not sure if this is the exact answer you want, but we can use fractions to determine how much one drink tastes compared to the other.

For Sam's Friday drink, we see that he makes 7 liters of orange soda by mixing 3 liters of orange juice with 4 liters of soda. As such, we know that
`(3-liters-of-orange-juice)/(7-total-liters)` and
`(4-liters-of-soda)/(7-total-liters)`.

For Sam's Saturday drink, we can also approach it the same way: the drink has
`(4-liters-of-orange-juice)/(9-total-liters)` and
`(5-liters-of-soda)/(9-total-liters)`

Now, we can just compare the fractions with each other:

`(4-liters-of-orange-juice)/(9-total-liters)` >
`(3-liters-of-orange-juice)/(7-total-liters)` and

`(4-liters-of-soda)/(7-total-liters)` >
`(5-liters-of-soda)/(9-total-liters)`.

So we know that the Saturday drink will probably taste more like orange juice than the Friday one. Conversely, we know that the Friday drink will probably taste more like soda than the Saturday one.